Simplified and two-stage quasi-likelihood estimators
J E Hutton, O.T. Ogunyemi, Paul I. Nelson · 1991
Abstract Properties of a quasi-likelihood estimator are typically obtained from an expansion of the quasi-likelihood in which the remainder term is asymptotically negligible. The remainder term, however, can be very difficult to control in some important applications, especially in models where both the mean and variance depend on the unknown parameter. In such cases we propose a modified quasi-likelihood based on the use of a simplified covariance matrix. Conditions for the consistency and asymptotic normality of the resulting estimators are developed. We illustrate this approach with a branching process with immigration model and present a simulation study of the small sample behaviour of the estimators.